Stochastic Penna model for biological aging

Summary A stochastic genetic model for biological aging is introduced bridging the gap between the bit-string Penna model and the Pletcher-Neuhauser approach. The phenomenon of exponentially increasing mortality function at intermediate ages and its deceleration at advanced ages is reproduced for both the evolutionary steady-state population and the genetically homogeneous individuals.     

Approximate analytical solutions of root surface nutrient uptake flux and rhizosphere solute concentrations

该文用Nye-Tinker-Barber模型来研究植物根系表面的养分吸收通量和根围溶质浓度的近似解析解。将根围区域分为远场区域和近场区域, 在远场用相似变量, 在近场用尺度变换, 将远场解在根表面展开并与近场解进行待定函数的匹配, 从而获得对流扩散方程根表面通量和浓度的一阶近似解析解, 该解能够简化到扩散方程的解的形式。对氮、钾、硫、磷、镁、钙的养分吸收通量和氮、钾的浓度分别进行数值模拟, 比较模型的数值解、Roose的近似解析解和该文的近似解析解。结果表明: 在扩散方程中, 6种元素通量的解析解与Roose解析解相近, 但均高于数值解, 钾和磷的通量在短时间内迅速衰减; 钾和氮浓度的全局近似解析解与Roose解析解接近, 并与数值解的变化趋势一致。在对流扩散方程中, 除氮外的5种元素通量的近似解较Roose的解析解更接近于数值解, 且没有奇性。     

An individual-based model applied to the study of different fishing strategies of Pintado Pseudoplatystoma corruscans (Agassiz, 1829)

The decline in stocks of commercial fish species has been documented in several regions of the world. This decline is due partially to the effect of evolutionary pressure caused by the management of fishing activity, which reduces the size of fish after a few generations. In this paper, the population dynamics of the Pintado Pseudoplatystoma corruscans, one of the main commercial species of freshwater fish in Brazil, were simulated considering different scenarios of fishing mortality and different minimum and maximum lengths of capture. The results show that selective fishing based on the different proposed selectivity curves can result in an evolution-mediated increase in the growth rate of the fish, the biomass and the catch. This suggests that appropriate changes in Brazilian legislation can contribute to the sustainability of fisheries and to conservation of the fish stocks exploited by man.     

根表面养分吸收通量和根围溶质浓度的近似解析解

该文用Nye-Tinker-Barber模型来研究植物根系表面的养分吸收通量和根围溶质浓度的近似解析解。将根围区域分为远场区域和近场区域, 在远场用相似变量, 在近场用尺度变换, 将远场解在根表面展开并与近场解进行待定函数的匹配, 从而获得对流扩散方程根表面通量和浓度的一阶近似解析解, 该解能够简化到扩散方程的解的形式。对氮、钾、硫、磷、镁、钙的养分吸收通量和氮、钾的浓度分别进行数值模拟, 比较模型的数值解、Roose的近似解析解和该文的近似解析解。结果表明: 在扩散方程中, 6种元素通量的解析解与Roose解析解相近, 但均高于数值解, 钾和磷的通量在短时间内迅速衰减; 钾和氮浓度的全局近似解析解与Roose解析解接近, 并与数值解的变化趋势一致。在对流扩散方程中, 除氮外的5种元素通量的近似解较Roose的解析解更接近于数值解, 且没有奇性。     

Biological ageing with birth rate controlled by mutations in the Penna model

Summary Within the Penna model, we assume a modification with a reproduction rate B that depends on the health state of the individual defined by the number of bad mutations. The idea is that biologically weaker individuals has got less chance to produce offsprings. The results obtained from simulations and for typical set of model parameters show that then the mortality rate q(a) is increasing faster with age a. The maximum age is also limited from about 50 percent of the biological maximum life-span for the standard Penna model, to about 40 percent. We also conclude that bad mutation distribution r(a) is altered so that younger individuals may accommodate significantly more bad mutations, up to 25 percent, as compared with the standard model (5 percent). In summary, it makes sense to force less productivity for older and weaker individuals.     

Stability of a model of human granulopoiesis using continuous maturation

A class of mathematical models involving a convection-reaction partial differential equation (PDE) is introduced with reference to recovering human granulopoiesis after high dose chemotherapy with stem cell support. The stability properties of the model are addressed by means of numerical investigations and analysis. A simplified model with proliferation rate and mobilization rate independent of maturity shows that the model is stable as the maturation rate grows without bounds, but may go through stable and non-stable regimens as the maturation rate varies. It is also shown that the system is stable when parameters are chosen to approximate a real physiological situation. System characteristics do not change profoundly by introduction of a maturity-dependent proliferation and mobilization rate, as is necessary to make the model operate more in accordance with hematological observations. However, by changing the system mitotic responsiveness with respect to changes in cytokine level, the system is still stable but may show persistent oscillations much resembling clinical observations of cyclic neutropenia. Furthermore, in these cases, changes in the model feedback signal caused by, for instance, an impaired effective cytokine elimination by cell receptors may enforce these oscillations markedly.     

Approximated solution of model for three-phase fluidized bed biofilm reactor in wastewater treatment

An approximated analytical solution of mathematical model for the three phase fluidized bed bioreactor (TFBBR) was proposed using the linearization technique to describe oxygen utilization rate in wastewater treatment. The validation of the model was done in comparison with the experimental results. Satisfactory agreement was obtained in the comparison of approximated analytical solution and numerical solution in the oxygen concentration profile of a TFBBR. The approximated solutions for three modes of the liquid phase flow were compared. The proposed model was able to predict the biomass concentration, dissolved oxygen concentration the height of efficient column, and the removal efficiency.     

Analytical solution for a hybrid Logistic-Monod cell growth model in batch and continuous stirred tank reactor culture

Monod and Logistic growth models have been widely used as basic equations to describe cell growth in bioprocess engineering. In the case of the Monod equation, the specific growth rate is governed by a limiting nutrient, with the mathematical form similar to the Michaelis–Menten equation. In the case of the Logistic equation, the specific growth rate is determined by the carrying capacity of the system, which could be growth-inhibiting factors (i.e., toxic chemical accumulation) other than the nutrient level. Both equations have been found valuable to guide us build unstructured kinetic models to analyze the fermentation process and understand cell physiology. In this work, we present a hybrid Logistic-Monod growth model, which accounts for multiple growth-dependent factors including both the limiting nutrient and the carrying capacity of the system. Coupled with substrate consumption and yield coefficient, we present the analytical solutions for this hybrid Logistic-Monod model in both batch and continuous stirred tank reactor (CSTR) culture. Under high biomass yield (Y_x/s) conditions, the analytical solution for this hybrid model is approaching to the Logistic equation; under low biomass yield condition, the analytical solution for this hybrid model converges to the Monod equation. This hybrid Logistic-Monod equation represents the cell growth transition from substrate-limiting condition to growth-inhibiting condition, which could be adopted to accurately describe the multi-phases of cell growth and may facilitate kinetic model construction, bioprocess optimization, and scale-up in industrial biotechnology.     

修正Camassa-Holm方程尖峰孤波解的稳定性

通过对具有哈密顿结构的修正Camassa-Holm方程的三个守恒量进行先验估计,算子谱分析,讨论了尖峰孤波解的稳定性取决于d″（c）的符号,并且给出d″（c）的具体表达式.借此给出修正Camassa-Holm方程的尖峰孤波解的稳定性与速度c有关,即c〉0,孤波解稳定,c〈0,孤波解不稳定;推广了[2]中相应的结论.     

A mathematical model of a crocodilian population using delay-differential equations

The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong age-dependence. We develop delay-differential equation (DDE) models describing the evolution of a crocodilian population. In using the delay formulation, we are able to account for both the TSD and the age-dependence of the life parameters while maintaining some analytical tractability. In our single-delay model we also find an equilibrium point and prove its local asymptotic stability. We numerically solve the different models and investigate the effects of multiple delays on the age structure of the population as well as the sex ratio of the population. For all models we obtain very strong agreement with the age structure of crocodilian population data as reported in Smith and Webb (Aust. Wild. Res. 12, 541-554, 1985). We also obtain reasonable values for the sex ratio of the simulated population.     

Exact solution of the multi-allelic diffusion model

We give an exact solution to the Kolmogorov equation describing genetic drift for an arbitrary number of alleles at a given locus. This is achieved by finding a change of variable which makes the equation separable, and therefore reduces the problem with an arbitrary number of alleles to the solution of a set of equations that are essentially no more complicated than that found in the two-allele case. The same change of variable also renders the Kolmogorov equation with the effect of mutations added separable, as long as the mutation matrix has equal entries in each row. Thus, this case can also be solved exactly for an arbitrary number of alleles. The general solution, which is in the form of a probability distribution, is in agreement with the previously known results. Results are also given for a wide range of other quantities of interest, such as the probabilities of extinction of various numbers of alleles, mean times to these extinctions, and the means and variances of the allele frequencies. To aid dissemination, these results are presented in two stages: first of all they are given without derivations and too much mathematical detail, and then subsequently derivations and a more technical discussion are provided.     

Stability of stationary distributions in a space-dependent population growth process

We consider a spatial population growth process which is described by a reaction-diffusion equation c(x)u _t = (a ²(x)u _x ) _x +f(u), c(x) >0, a(x) > 0, defined on an interval [0, 1] of the spatial variable x. First we study the stability of nonconstant stationary solutions of this equation under Neumann boundary conditions. It is shown that any nonconstant stationary solution (if it exists) is unstable if a _xx0 for all x[0, 1], and conversely ifa _xx>0 for some x[0, 1], there exists a stable nonconstant stationary solution. Next we study the stability of stationary solutions under Dirichlet boundary conditions. We consider two types of stationary solutions, i.e., a solution u ₀(x) which satisfies u ₀ x0 for all x[0, 1] (type I) and a solution u ₀(x) which satisfies u _0x = 0 at two or more points in [0, 1] (type II). It is shown that any stationary solution of type I [type II] is stable [unstable] if a _xx 0 [a _xx 0] for all x[0, 1]. Conversely, there exists an unstable [a stable] stationary solution of type I [type II] if a _xx <0 [a _xx >0] for some x[0, 1].     

A mathematical model of biological evolution

In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dN _n (t)/dt=(m _n (t-)N _n (t)+N _n-1(t) (n=0,1,2,3...), where N _n (t) and m _n (t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by is rigorously obtained for the case (i) m _n (t)=m _n is independent of t (constant fitness model), where m _n is essentially periodic with respect to n, and for the case (ii) (periodic fitness model), together with the long time average m of the average Malthusian parameter . The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations.An early version of this study was read at the International Symposium on Mathematical Topics in Biological held in kyoto, Japan, on September 11–12, 1978, and was published in its Procedings.     

应用修正的Gash解析模型对岷江上游亚高山川滇 高山栎林林冠截留的模拟

修正的Gash解析模型具有较好的物理基础,是目前估算和预测林冠截留的有效工具。基于2007年6月到9月的降雨数据、气象和林分结构资料,采用修正的Gash解析模型对岷江上游川滇高山栎林冠截留进行了模拟。结果表明,林冠持水能力为0.23mm,树干持水能力为0.041mm,树干茎流系数为0.013,使林冠饱和的降雨为0.3mm;研究期间实测的林冠截留量为80.2mm,占总降雨量的16.5%,应用模型模拟的林冠截留总量为81.8mm,高于实测值1.6mm(高于实测值2.0%),林冠截留和树干茎流周累积量模拟值均与实测值有很好的一致性,敏感性分析结果显示,应用修正的Gash解析模型进行岷江上游川滇高山栎林冠截留模拟研究中,模型最易受林冠持水能力影响,其次为郁闭度、树干持水能力,影响最小的林分参数为树干茎流系数。     

人口动力学中非线性发展方程解的爆破现象

讨论描述人口发展规律的一类非线性发展方程具有第三类非线性边界条件的混合问题．在已知函数满足某些假设条件下,证明了其解在有限时间内爆破．     

Towards an analytical model of soft biological tissues

In the past years, soft-tissue modelling research has seen substantial developments, a significant part of which can be ascribed to the refinement of numerical techniques, such as Finite Element analysis. A large class of physico-mechanical properties can be effectively simulated and predictions can be made for a variety of phenomena. However, there is still much that can be conceptually explored by means of fundamental theoretical analysis. In the past few years, driven by our interest in articular cartilage mechanics, we have developed theoretical microstructural models for linear elasticity and permeability that accounted for the presence and arrangement of collagen fibres in cartilage. In this paper, we investigate analytically the non-linear elasticity of soft tissues with collagen fibres arranged according to a given distribution of orientation, a problem that, aside from the case of fibres aligned in a finite number of distinct directions, has been treated exclusively numerically in the literature. We show that, for the case of a tissue with complex fibre arrangement, such as articular cartilage, the theoretical framework commonly used leads to an integral expression of the elastic strain energy potential. The present model is a first attempt in the development of a unified analytical microstructural model for non-linear elasticity and permeability of hydrated, fibre-reinforced soft tissues.     

一类时滞种群系统周期正解的稳定性

本文利用重合度论研究了一类时滞种群系统周期正解的存在性、唯一性及稳定性．     

Role of nuclear analytical probe techniques in biological trace-element research

Many biomedical experiments require the qualitative and quantitative localization of trace elements with high sensitivity and good spatial resolution. The feasibility of measuring the chemical form of the elements, the time course of trace element metabolism, and conducting experiments in living biological systems are also important requirements for biological trace element research. Nuclear analytical techniques that employ ion or photon beams have grown in importance in the past decade and have led to several new experimental approaches. Some of the important features of these methods are reviewed here along with their role in trace element research. Examples of their use are given to illustrate potential for new research directions. It is emphasized that the effective application of these methods necessitates a closely integrated multidisciplinary scientific team.     

Stability analysis of the partial selfing selection model

We undertake a detailed study of the one-locus two-allele partial selfing selection model. We show that a polymorphic equilibrium can exist only in the cases of overdominance and underdominance and only for a certain range of selfing rates. Furthermore, when it exists, we show that the polymorphic equilibrium is unique. The local stability of the polymorphic equilibrium is investigated and exact analytical conditions are presented. We also carry out an analysis of local stability of the fixation states and then conclude that only overdominance can maintain polymorphism in the population. When the linear local analysis is inconclusive, a quadratic analysis is performed. For some sets of selective values, we demonstrate global convergence. Finally, we compare and discuss results under the partial selfing model and the random mating model.